Some Results on Controlled K−Frames in Hilbert Spaces

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also K-frames have been introduced to study atomic systems with respect to bounded linear operator. In this paper, the notion of controlled K-frames will be studied and it will be shown that controlled K-frames are equivalent to K-frames under some mild conditions. Finally, the stability of controlled K-Bessel sequences under perturbation will be discussed with some examples.